Add each column from right to left. If the answer from a column is one digit, write it under that column. If the answer is 2 digits, then write down the ones place from the answer and carry the tens to the next column. As you add from right to left, if you have carried, combine that number with the rest of the column numbers.
Subtracting Whole Numbers
Subtract each column from right to left. If the column on top is smaller than the bottom then borrow 1 group from the column to the left. Subtract that column then move on to the next column to the left.
Multiplying Whole Numbers
Multiply the top number from right to left by the ones digit on the bottom row. If the answer for a product is 2 digits, then write down the ones digit and carry the tens digit to the next column. Continue until the top number has been multiplied by the bottom. Because the tens digit on the bottom is really a group of ten, putting a place holding zero under the first digit in the first row and then multiply and tens digit from the bottom row as if it were a single digit. Last step, add the two rows together following the whole number addition steps.
Long Divide Whole Numbers
Ask, "How many times does the divisor (outside number) go into the first digit inside the bar?" If the divisor is larger than the first digit of the dividend (inside number) then put a zero up on top of the bar in the quotient. After you divide, then multiply the number that you put in the quotient (on top of the division sign) by the divisor on the side. Subtract that number from the number you divided (dividend). Check to see if the difference (the subtraction answer) is less than the divisor. If it is, then bring down the next digit from the dividend and start dividing again. When you subtract for the last time, put that answer as the remainder.
Adding Decimals
Line up decimals vertically and then add zeroes to the right to make all the columns end in the same place. Add like whole numbers then bring the decimal straight down. If you have a whole number, the decimal should be placed to the right of it.
Subtracting Decimals
Line up decimals vertically. Whole numbers have a decimal to the right of the number. If the top number is shorter than the bottom, fill in with zeroes so you have something to borrow from. Subtract like whole number subtraction and bring the decimal down into the answer.
Multiplying Decimals
Multiply like whole numbers. Then count the number of decimal places in the factors (the problem). After the multiplication is finished, place the decimal so you have the same number of decimal places in the answer (product) as you did in the factors, total.
Prime Factorization
Divide the given number by any prime number that will evenly divide it. Continue this process until the answer to the division problem is a prime number. List all of these prime factors in order from smallest to largest with multiplication signs in between.
Rounding to the Nearest Tenths or Hundredths
Leave all digits to the left the same. Look at the column you're asked to round and then either leave it the same or round up one if the next column to the right is 5 or larger. Once you have done this, the answer ends in the column you were asked to round.
Order of Operations
Use the PEMDAS model and do ( ) from left to right. Then exponents. Then multiply and divide FROM LEFT TO RIGHT. Then add and subtract FROM LEFT TO RIGHT.
Mastery Skill Explanations
Adding Whole Numbers
Add each column from right to left. If the answer from a column is one digit, write it under that column. If the answer is 2 digits, then write down the ones place from the answer and carry the tens to the next column. As you add from right to left, if you have carried, combine that number with the rest of the column numbers.
Subtracting Whole Numbers
Subtract each column from right to left. If the column on top is smaller than the bottom then borrow 1 group from the column to the left. Subtract that column then move on to the next column to the left.
Multiplying Whole Numbers
Multiply the top number from right to left by the ones digit on the bottom row. If the answer for a product is 2 digits, then write down the ones digit and carry the tens digit to the next column. Continue until the top number has been multiplied by the bottom. Because the tens digit on the bottom is really a group of ten, putting a place holding zero under the first digit in the first row and then multiply and tens digit from the bottom row as if it were a single digit. Last step, add the two rows together following the whole number addition steps.
Long Divide Whole Numbers
Ask, "How many times does the divisor (outside number) go into the first digit inside the bar?" If the divisor is larger than the first digit of the dividend (inside number) then put a zero up on top of the bar in the quotient. After you divide, then multiply the number that you put in the quotient (on top of the division sign) by the divisor on the side. Subtract that number from the number you divided (dividend). Check to see if the difference (the subtraction answer) is less than the divisor. If it is, then bring down the next digit from the dividend and start dividing again. When you subtract for the last time, put that answer as the remainder.
Adding Decimals
Line up decimals vertically and then add zeroes to the right to make all the columns end in the same place. Add like whole numbers then bring the decimal straight down. If you have a whole number, the decimal should be placed to the right of it.
Subtracting Decimals
Line up decimals vertically. Whole numbers have a decimal to the right of the number. If the top number is shorter than the bottom, fill in with zeroes so you have something to borrow from. Subtract like whole number subtraction and bring the decimal down into the answer.
Multiplying Decimals
Multiply like whole numbers. Then count the number of decimal places in the factors (the problem). After the multiplication is finished, place the decimal so you have the same number of decimal places in the answer (product) as you did in the factors, total.
Prime Factorization
Divide the given number by any prime number that will evenly divide it. Continue this process until the answer to the division problem is a prime number. List all of these prime factors in order from smallest to largest with multiplication signs in between.
Rounding to the Nearest Tenths or Hundredths
Leave all digits to the left the same. Look at the column you're asked to round and then either leave it the same or round up one if the next column to the right is 5 or larger. Once you have done this, the answer ends in the column you were asked to round.
Order of Operations
Use the PEMDAS model and do ( ) from left to right. Then exponents. Then multiply and divide FROM LEFT TO RIGHT. Then add and subtract FROM LEFT TO RIGHT.